OPSM 405 Service Management Koç University OPSM 405 Service Management Class 16: Yield management: overbooking Zeynep Aksin zaksin@ku.edu.tr

Yield Management System Reservation System current demand cancellations Forecasting cancellation rate estimates future demand estimates Overbooking Levels overbooking levels Discount Allocation fare class allocations

Dealing with cancellations Overbooking control total cost Basic Problem: E[Rev] $ opportunity cost of unsold seats overbooking costs capacity overbooking limit (BL) #seats sold

Overbooking Two basic costs: Stock outs Overage customers have a reservation and there are no rooms left Overage customers denied advance reservation and rooms are unoccupied

Example: Hotel California Stock outs: 0.8 x $150 = $120 Overage: $50

Table 9.1: Hotel California No-Show Experience No-Shows % of Experiences Cumulative % of Experiences 0 5 5 1 10 15 2 20 35 3 15 50 4 15 65 5 10 75 6 5 80 7 5 85 8 5 90 9 5 95 10 5 100

Overbooking Approach 1: Using Averages In Table 9.1 the average number of no-shows is calculated by 0x0.05 + 1x0.10 + 2x0.20 + 3x0.15 +…+ 10x0.05 = 4.05. Take up to four overbookings.

Overbooking Approach 2: Spreadsheet Analysis

Book more guests until: Overbooking Approach 3: Marginal Cost Approach Book more guests until: E(cost of dissatisfied customer) = E(cost of empty room) Cost of dissatisfied customer * Probability that there are fewer no-shows than overbooked rooms = Cost of empty room * Probability that there are more no-shows than overbooked rooms

Hotel California Co/(Cs + Co) = P(Overbook  No Shows) Hotel Data 29% Overbook 2 rooms Table 9.1: Hotel California No-Show Experience No-Shows % of Experiences Cumulative % of Experiences 0 5 5 1 10 15 2 20 35 29%

Overbooking: Marginal analysis n-th cust shows up? +$r p yes no 1-p Seat available for n-th cust.? $0 yes Accept n-th request? no n-th cust shows up? yes p -$s yes no 1-p no $0 $0 N(n,p) is binomial r.v. with parameters n,p

Accept if ...

Example

Dynamic Overbooking Overbooking Time to Event Event Occurs Reservations Start

Overbooking over time %Capacity 100% 90 days to departure o booking limit reservations with overbooking 100% reservations without overbooking 90 days to departure o

Bulvar Palas The contribution of each room is 40YTL per night. If a guest holding a reservation is turned away owing to overbooking, then other costs are incurred: Arrangements with a nearby hotel Penalties associated with lost good will Management estimates this cost as 100YTL per guest “walked”

Bulvar Palas No-Show Experience: (Daily) Example: Bulvar Palas Bulvar Palas No-Show Experience: (Daily) No-shows Probability P[no show] Cum. Prob. P[no show<x] 0 0.07 0.00 1 0.19 0.07 2 0.22 0.26 3 0.16 0.48 4 0.12 0.64 5 0.10 0.76 6 0.07 0.86 7 0.04 0.93 8 0.02 0.97 9 0.01 0.99

Marginal analysis How much can I overbook? Overbook too few 40YTL, P(no show>x) Overbook too many 100YTL, P(no show<x) Keep overbooking as long as 40*P(no show>x) > 100*P(no show<x) or P(no show<x) < 40/(40+100)=0.286 Overbook 2 rooms based on no-show distribution

Example The Ozhas bus company is currently assessing its Istanbul-Adana run. The number of customers that do not show up after making a reservation are uniformly distributed from 1 to 10. Tickets costs are 45YTL, and if a particular bus run is full, a passenger with a reservation is given passage on a rival company’s bus at a cost of 75YTL. Using the averages method, what should Ozhas’s overbooking policy be?

Averages method Using the averages method, the average number of no shows is calculated by: 0(0.0)+1(0.1)+2(0.1)+3(0.1)+4(0.1)+5(0.1)+6(0.1)+7(0.1)+8(0.1)+9(0.1)+10(0.1) = 5.5

Spreadsheet approach No shows Probability 1 2 3 4 5 6 7 $0 ($75) $45 Cs = $75 Number of Reservations Overbooked No shows Probability 1 2 3 4 5 6 7 $0 ($75) ($150) ($225) ($300) ($375) ($450) ($525) 0.1 ($45) ($90) ($135) ($180) ($270) ($315) 8 ($360) 9 ($405) 10 Total cost ($248) ($203) ($170) ($149) ($140) ($143) ($158) ($185)

Likya World Number of customers who book a night and fail to show up is Normally distributed with mean 20 and standard deviation 10 Bumping a customer costs 300 YTL If room is not sold, hotel loses revenue of 105 YTL

Likya World 105/(300+105)=0.2592 Look up in a standard normal table to obtain z=-0.645 So number of seats to overbook= 20-0.645*10=13.5 Alternatively use NORMINV(0.2592,20,10)

Obtaining the Probability Standardized Normal Probability Table (Portion) Z .00 .01 .02 s = 1 0.0 .50000 .50399 .50798 Z : : : : 2.0 .97725 .97784 .97831 .97725 m = 0 2.0 Z 2.1 .98214 .98257 .98300 z Probabilities in body